f -Biharmonic Submanifolds in Space Forms and f -Biharmonic Riemannian Submersions from 3-Manifolds

Ze-Ping Wang () and Li-Hua Qin
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Ze-Ping Wang: School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China
Li-Hua Qin: School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China

Mathematics, 2024, vol. 12, issue 8, 1-16

Abstract: f -biharmonic maps are generalizations of harmonic maps and biharmonic maps. In this paper, we give some descriptions of f -biharmonic curves in a space form. We also obtain a complete classification of proper f -biharmonic isometric immersions of a developable surface in R 3 by proving that a proper f -biharmonic developable surface exists only in the case where the surface is a cylinder. Based on this, we show that a proper biharmonic conformal immersion of a developable surface into R 3 exists only in the case when the surface is a cylinder. Riemannian submersions can be viewed as a dual notion of isometric immersions (i.e., submanifolds). We also study f -biharmonicity of Riemannian submersions from 3-manifolds by using the integrability data. Examples are given of proper f -biharmonic Riemannian submersions and f -biharmonic surfaces and curves.

Keywords: biharmonic maps; f -biharmonic maps; Riemannian submersions; f -biharmonic curves; f -biharmonic submanifolds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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